Introduction to Weight Transfer

What is weight transfer?

When you apply any kind of force on the car, whether it be acceleration, braking, or cornering, the car will transfer weight from one end or side of the car to the other. A Volkswagen three wheeling it through a hard turn clearly has no weight on the inside back tire, as it's several inches in the air! In this discussion, we'll be looking at the reasons and effects of weight transfer and try to understand how this affects the dynamics of the car.

A couple of clarifications to start with: I will be using the small-angle assumption sin(f)=f in order to simplify the equations. I will also refer to the front and rear suspensions as 'half-suspensions', so if I use that term, it means either the front or rear suspension, or both, but taken independently of the other. Also, this discussion deals only with independent suspensions, particularly the Short-Long Arm (SLA) or 'double-wishbone' as found on the 2nd generation (2G) DSM's. It also applies, in general, to the strut-type suspension on the 1st generation (1G) DSM.

Why does weight transfer?

Weight transfer is due to the most basic of the Laws of Physics, Newton's Laws. Newton's First Law states: "An object at rest remains at rest until acted upon by a force. An object in motion continues moving in a straight line at constant velocity until acted upon by a force."

Your car, being the body in question, has inertia, and will resist being made to change course or speed. The heavier the car, the more inertia it has, and the more resistant to change it will be. This 'resistance' acts through the "center of gravity" (or center of mass) of the car. In cornering, this is called 'centrifugal force'. The center of gravity (CG) of the car is the point where, if you could hold it by the CG, it would not rotate. In a typical passenger car, the CG is about 35-40% of the way behind the front wheels, and about 500-550mm above the ground.

The forces making the car turn or brake or accelerate act through the contact patch, where the tires meet the pavement. This presents a problem because a car's center of gravity is above the ground, while the contact patch is on the ground. This sets up a 'moment', or a pair of unbalanced forces that produce a rotation about the car's center of gravity. The rotation forces one side of the car down, and lifts up on the other side, effectively transferring weight from one side to the other.

What about body roll?

Once weight begins to transfer, the body of the car reacts. The suspension will rotate about the 'Roll Center', which is determined by the suspension geometry. If you picture a simple pinwheel, the roll center is the pin in the middle, and coincides with the center of gravity. However, a pendulum's roll center is at the top of the pendulum, while the CG is near the bottom end.

To find the roll center of a Short/Long-Arm (SLA) suspension, like that of the 2nd gen DSM, find the intersection of the line of the upper and lower control arms, and draw a line from that point to the center of the contact patch. Do this for both sides, and where the two lines intersect is the roll center. If both sides are symmetrical, the roll center will be along the car centerline.

If the roll center is below the center of gravity, which is the case in almost all cars, the car will rotate to the outside of the turn. The car rolls by compressing the springs on the outside of the turn, while the springs on the inside of the turn extend. The car will rotate until the force of the springs balance the new weight distribution.

If the roll center is above the center of gravity, the car will rotate into the turn. Very few cars are able to get the CG low enough and the roll center high enough to do this, and there are other problems associated with this configuration. If the roll center is at the same height as the CG, there will be no body roll. While at first this would seem like a good idea, it turns out to be not so great. The reason for this will be discussed in later in this article.

In most passenger cars, the rear roll center will be at or above the front roll center. For the 2G DSM, the front roll center is about 73mm above the ground at the stock ride height, while the rear is at about 83mm. The 'Roll Axis' is a line drawn between the roll centers of the front and rear suspensions. This is the axis about which the car rolls.

How much weight transfers?

The percentage of weight transfer is governed by the following equation:

Equation 1:

Where: W is the sprung weight of the car a is the cornering acceleration in g's hCG is the height of the center of gravity t is the track width of the car

Even if the car has no roll (due to the roll center coinciding with the CG, or simply a car with no suspension), the same amount of weight will still transfer. The height of the CG and the track width (measured from the center of one tire's contact patch to the other) determine the amount of weight transfer.

There is also a secondary effect caused by the lateral movement of the CG as the body rolls:

Equation 2:

Where: f   is the roll angle of the car in radians, hCG is the height of the center of gravity, ha is the height of the roll axis at the CG.

This value is small in comparison to Equation 2. Given a CG height of around 500mm, and a track width of 1500mm, a roll angle of 5º and a roll axis height of 100mm, the weight transfer is on the order of 2% per g of acceleration. This term is normally neglected in weight transfer calculations.

OK, so why do we care about weight transfer?

Weight transfer affects the amount of traction. The traction of a tire increases as the weight on the tire increases, at least up to the load limit of the tire. The problem is, it does not increase linearly. So, as weight transfers from the inside tire to the outside tire, the inside tire loses traction faster than the outside tire gains it, resulting in a net reduction in overall traction.

Where do the springs enter into all this?

Changing our frame of reference from the ground to the roll center, the weight transfer can also be expressed by the following equation:

Equation 3:

Where: W is the sprung weight (front or rear, as determined by the weight distribution of the car), Kf is the roll stiffness of the suspension.

If we look at the effects of this equation, it becomes more clear. Remember, the total equation still has to equal Equation 1. As the roll center height approaches zero, the first half of the equation goes to zero, and weight transfer only happens as a function of the roll of the car. If, however, the roll center height approaches the height of the CG, then f   goes to zero (see Equation 6), and weight transfer in only due to the cornering forces acting through the control arms.

Part one of this equation is the weight transfer due to cornering forces. Since this portion of the equation is derived from the lateral force on the suspension, acting through the control arms. It is an instantaneous effect. CG height and roll angle have no effect on this, nor do the springs.

The second part of this equation is due to the car's roll, acting through the springs. It is dependent on the suspension's dynamics and in some cases may lag behind the cornering forces. For example, in a transient maneuver like a slalom where the car is being turned from side to side rapidly, f  may be negative. If the car is rolling right after a left hand turn, and you suddenly swerve to the right, the body roll becomes out of phase with the cornering force. This reduces the overall weight transfer for a moment, but also becomes dangerous as the body roll will eventually reverse itself, and may do so suddenly and violently.

Equation 3 is also valid for each half-suspension:

Equation 4:	Where: Kf f  is the roll stiffness of the front suspension, Wf is the sprung weight on the front suspension, hf is the front roll center height, tf is the front track width.
Equation 5:	Where: Kf r  is the roll stiffness of the rear suspension, Wr is the sprung weight on the rear suspension, hr is the rear roll center height, tr is the rear track width.

These two equations give us our weight transfer distribution. Since the total weight transfer remains the same, by changing the characteristics at one end of the car Raising or lowering the roll center at one end will change the weight transfer distribution as well. Raising the roll center at the rear, for example, will increase weight transfer at that end, and reduce understeer. This technique is also used to provide a softer ride by raising the rear roll center while softening the rear springs, resulting in the same roll and similar handling, with a more comfortable ride.

Notice that K_f appears in the numerator on the right. This means that a stiffer suspension transfers more weight per degree of roll. It makes sense if you think of a car that is so stiffly sprung it does not roll hardly at all. It still has to transfer the same amount of weight as given in Equation 1 as if it were softly sprung, but has less roll to do it with. When taken in the context of front and rear half-suspensions, whichever end of the car is stiffer will transfer more of it's sprung weight! This gives us the capability to control the under- or over-steer characteristics of the car by changing the stiffness at one end of the car. Stiffening the rear will create more weight transfer in the rear, reducing traction at that end, and reducing understeer. Reducing the front roll stiffness will reduce front weight transfer, increasing traction, and reducing understeer. It is important to keep the front suspension from bottoming out, however, because if the front bottoms out, the roll stiffness skyrockets, greatly increasing front weight transfer, and causing the car to understeer or 'push'.

The Roll Angle, f, is governed by the following equation:

Equation 6:

Where: hCG is the height of the center of gravity, ha is the height of the roll axis at the CG, Kf is the front roll stiffness, Kr is the rear roll stiffness.

The term (h_CG - h_a) is the 'Roll Couple', or the vertical distance from the center of gravity to the roll axis. The shorter the Roll Couple, the smaller the roll angle!

So, all I have to do is raise the roll center, and that solves the body roll problem?

Body roll is bad when the suspension cannot compensate for it and the outside tires begin to tilt beyond vertical (positive camber relative to the ground). It is also important not to have so much body roll that the suspension bottoms out and hits the bump-stops. But, because the roll angle, combined with the front/rear roll stiffness distribution, allows us to adjust the over-/under-steer characteristics, this makes it impossible to tune a car with a roll center height near the CG height! A higher roll center also means more 'jacking force'.

In the diagram on the right, you see the effect of two different roll centers. The car is facing out of the page, and it is turning to the right. The cornering force acts through the roll center, producing a 'push' from the outside tire (in blue), and a 'pull' from the inside tire (in yellow). Because weight is transferring from the inside to the outside tire, the outside tire is generating more cornering force. The horizontal components are, of course, canceled by the inertia force on the CG. The vertical components would cancel out if the tires were generating the same cornering force, but since the outside tire's force is greater, there is a net force upward. This force attempts to lift or 'jack' the car upward. The higher the roll center and the greater the difference between inside and outside cornering forces, the greater the jacking force. This is most evident on the rear end of cars with a 'swing-axle' independent rear suspension, like the VW Beetle, the early Triumph Spitfire, and the Chevrolet Corvair. The jacking force reduces traction, and it the main reason for keeping the roll center low.

What happens to the roll center when the body rolls?

Well, to complicate things, the roll center not only moves up and down, but it also moves left or right! In the diagram on the right, you can see the effect of 7.6° of roll on a 2G front suspension. Using the intersection of the control arms and the contact patch, we can easily find the new location of the roll center. Note that the inside suspension control arms are very nearly parallel, and the intersection point is far off the page. The roll center has moved up from about 74mm above the ground to 83mm, and has moved 300mm to the inside of the turn. You can also see the camber of the tires relative to the ground. The inside tire (in yellow) has very little contact patch, and the outside tire (in blue) is beginning to lean past vertical.

Lateral movement of the roll center isn't necessarily a bad thing. By moving the roll center toward the inside of the turn, it decreases the upward movement of the inside suspension while increasing the downward movement of the outside suspension. This causes the car to 'hunker down' in the turn, instead of feeling 'tippy'.

So that's it?

All that being said, it becomes difficult to modify a production car to change the roll center. Lowering the car with springs will lower the roll center by almost the same amount. Lowering the car using a shorter tire will lower the roll center the same amount. Modifying the lower control arm mounts to change the roll center can be effective, but also changes the geometry of the suspension and changes the camber curves. But hopefully this has given you a better understanding of the mechanisms of weight transfer.

The 2G Suspension in both roll and steer

Back to the 2G Turn Harder Page

References:

Fundamentals of Vehicle Dynamics - Thomas Gillespie

Performance Handling, by Don Alexander